PHOTO: AFP
The tourists, who resumed on 20-1 chasing a victory target of 244, were shot out for 171 in the post-lunch session of the fifth day's play at the P. Sara Oval in Colombo.
Veteran Herath finished with four for 56 and Siriwardana took three for 25 to wreck the tourists, for whom Darren Bravo played a lone hand with 61.
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The West Indies slipped to 138 for nine before the last-wicket pair of Kemar Roach (13) and Jomel Warrican (20 not out) put on 33 runs to hand a batting lesson to their team-mates.
Sri Lanka, who had won the first Test in Galle by an innings and six runs, clinched the trophy named after West Indies great Garfield Sobers and former Sri Lankan captain Michael Tissera.
Herath finished with 15 wickets in the series to take his tally to 293, nearing the 300-wicket mark achieved by only two Sri Lankan bowlers, world record holder Muttiah Muralitharan and Chaminda Vaas.
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When play resumed after the entire fourth day had been washed out, the overnight pair of Bravo and Shai Hope easily negotiated the Sri Lankan bowlers to carry the score to 80-1.
Siriwardana broke the 60-run stand by having Hope stumped for 35 soon after Bravo had celebrated his half-century with two sixes off Herath.
Off-spinner Dilruwan Perera removed Marlon Samuels for six through a catch by Angelo Mathews, before Siriwardana trapped Jermaine Blackwood leg-before for four.
Herath sealed West Indies' fate soon after lunch by removing former captain Denesh Ramdin (10) and Bravo in the same over, both falling to catches by Mathews.
Skipper Jason Holder was leg-before to Siriwardana for seven and Jerome Taylor holed out in the deep off Herath for one.
The two teams will next meet in three one-day internationals and two Twenty20 games.
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